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Wu's Color Quantizer
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| Having received many constructive comments and bug reports about my previous | |
| C implementation of my color quantizer (Graphics Gems vol. II, p. 126-133), | |
| I am posting the following second version of my program (hopefully 100% | |
| healthy) as a reply to all those who are interested in the problem. | |
| /********************************************************************** | |
| C Implementation of Wu's Color Quantizer (v. 2) | |
| (see Graphics Gems vol. II, pp. 126-133) | |
| Author: Xiaolin Wu | |
| Dept. of Computer Science | |
| Univ. of Western Ontario | |
| London, Ontario N6A 5B7 | |
| [email protected] | |
| Algorithm: Greedy orthogonal bipartition of RGB space for variance | |
| minimization aided by inclusion-exclusion tricks. | |
| For speed no nearest neighbor search is done. Slightly | |
| better performance can be expected by more sophisticated | |
| but more expensive versions. | |
| The author thanks Tom Lane at [email protected] for much of | |
| additional documentation and a cure to a previous bug. | |
| Free to distribute, comments and suggestions are appreciated. | |
| **********************************************************************/ | |
| #include<stdio.h> | |
| #define MAXCOLOR 256 | |
| #define RED 2 | |
| #define GREEN 1 | |
| #define BLUE 0 | |
| struct box { | |
| int r0; /* min value, exclusive */ | |
| int r1; /* max value, inclusive */ | |
| int g0; | |
| int g1; | |
| int b0; | |
| int b1; | |
| int vol; | |
| }; | |
| /* Histogram is in elements 1..HISTSIZE along each axis, | |
| * element 0 is for base or marginal value | |
| * NB: these must start out 0! | |
| */ | |
| float m2[33][33][33]; | |
| long int wt[33][33][33], mr[33][33][33], mg[33][33][33], mb[33][33][33]; | |
| unsigned char *Ir, *Ig, *Ib; | |
| int size; /*image size*/ | |
| int K; /*color look-up table size*/ | |
| unsigned short int *Qadd; | |
| void | |
| Hist3d(vwt, vmr, vmg, vmb, m2) | |
| /* build 3-D color histogram of counts, r/g/b, c^2 */ | |
| long int *vwt, *vmr, *vmg, *vmb; | |
| float *m2; | |
| { | |
| register int ind, r, g, b; | |
| int inr, ing, inb, table[256]; | |
| register long int i; | |
| for(i=0; i<256; ++i) table[i]=i*i; | |
| Qadd = (unsigned short int *)malloc(sizeof(short int)*size); | |
| if (Qadd==NULL) {printf("Not enough space\n"); exit(1);} | |
| for(i=0; i<size; ++i){ | |
| r = Ir[i]; g = Ig[i]; b = Ib[i]; | |
| inr=(r>>3)+1; | |
| ing=(g>>3)+1; | |
| inb=(b>>3)+1; | |
| Qadd[i]=ind=(inr<<10)+(inr<<6)+inr+(ing<<5)+ing+inb; | |
| /*[inr][ing][inb]*/ | |
| ++vwt[ind]; | |
| vmr[ind] += r; | |
| vmg[ind] += g; | |
| vmb[ind] += b; | |
| m2[ind] += (float)(table[r]+table[g]+table[b]); | |
| } | |
| } | |
| /* At conclusion of the histogram step, we can interpret | |
| * wt[r][g][b] = sum over voxel of P(c) | |
| * mr[r][g][b] = sum over voxel of r*P(c) , similarly for mg, mb | |
| * m2[r][g][b] = sum over voxel of c^2*P(c) | |
| * Actually each of these should be divided by 'size' to give the usual | |
| * interpretation of P() as ranging from 0 to 1, but we needn't do that here. | |
| */ | |
| /* We now convert histogram into moments so that we can rapidly calculate | |
| * the sums of the above quantities over any desired box. | |
| */ | |
| void | |
| M3d(vwt, vmr, vmg, vmb, m2) /* compute cumulative moments. */ | |
| long int *vwt, *vmr, *vmg, *vmb; | |
| float *m2; | |
| { | |
| register unsigned short int ind1, ind2; | |
| register unsigned char i, r, g, b; | |
| long int line, line_r, line_g, line_b, | |
| area[33], area_r[33], area_g[33], area_b[33]; | |
| float line2, area2[33]; | |
| for(r=1; r<=32; ++r){ | |
| for(i=0; i<=32; ++i) | |
| area2[i]=area[i]=area_r[i]=area_g[i]=area_b[i]=0; | |
| for(g=1; g<=32; ++g){ | |
| line2 = line = line_r = line_g = line_b = 0; | |
| for(b=1; b<=32; ++b){ | |
| ind1 = (r<<10) + (r<<6) + r + (g<<5) + g + b; /* [r][g][b] */ | |
| line += vwt[ind1]; | |
| line_r += vmr[ind1]; | |
| line_g += vmg[ind1]; | |
| line_b += vmb[ind1]; | |
| line2 += m2[ind1]; | |
| area[b] += line; | |
| area_r[b] += line_r; | |
| area_g[b] += line_g; | |
| area_b[b] += line_b; | |
| area2[b] += line2; | |
| ind2 = ind1 - 1089; /* [r-1][g][b] */ | |
| vwt[ind1] = vwt[ind2] + area[b]; | |
| vmr[ind1] = vmr[ind2] + area_r[b]; | |
| vmg[ind1] = vmg[ind2] + area_g[b]; | |
| vmb[ind1] = vmb[ind2] + area_b[b]; | |
| m2[ind1] = m2[ind2] + area2[b]; | |
| } | |
| } | |
| } | |
| } | |
| long int Vol(cube, mmt) | |
| /* Compute sum over a box of any given statistic */ | |
| struct box *cube; | |
| long int mmt[33][33][33]; | |
| { | |
| return( mmt[cube->r1][cube->g1][cube->b1] | |
| -mmt[cube->r1][cube->g1][cube->b0] | |
| -mmt[cube->r1][cube->g0][cube->b1] | |
| +mmt[cube->r1][cube->g0][cube->b0] | |
| -mmt[cube->r0][cube->g1][cube->b1] | |
| +mmt[cube->r0][cube->g1][cube->b0] | |
| +mmt[cube->r0][cube->g0][cube->b1] | |
| -mmt[cube->r0][cube->g0][cube->b0] ); | |
| } | |
| /* The next two routines allow a slightly more efficient calculation | |
| * of Vol() for a proposed subbox of a given box. The sum of Top() | |
| * and Bottom() is the Vol() of a subbox split in the given direction | |
| * and with the specified new upper bound. | |
| */ | |
| long int Bottom(cube, dir, mmt) | |
| /* Compute part of Vol(cube, mmt) that doesn't depend on r1, g1, or b1 */ | |
| /* (depending on dir) */ | |
| struct box *cube; | |
| unsigned char dir; | |
| long int mmt[33][33][33]; | |
| { | |
| switch(dir){ | |
| case RED: | |
| return( -mmt[cube->r0][cube->g1][cube->b1] | |
| +mmt[cube->r0][cube->g1][cube->b0] | |
| +mmt[cube->r0][cube->g0][cube->b1] | |
| -mmt[cube->r0][cube->g0][cube->b0] ); | |
| break; | |
| case GREEN: | |
| return( -mmt[cube->r1][cube->g0][cube->b1] | |
| +mmt[cube->r1][cube->g0][cube->b0] | |
| +mmt[cube->r0][cube->g0][cube->b1] | |
| -mmt[cube->r0][cube->g0][cube->b0] ); | |
| break; | |
| case BLUE: | |
| return( -mmt[cube->r1][cube->g1][cube->b0] | |
| +mmt[cube->r1][cube->g0][cube->b0] | |
| +mmt[cube->r0][cube->g1][cube->b0] | |
| -mmt[cube->r0][cube->g0][cube->b0] ); | |
| break; | |
| } | |
| } | |
| long int Top(cube, dir, pos, mmt) | |
| /* Compute remainder of Vol(cube, mmt), substituting pos for */ | |
| /* r1, g1, or b1 (depending on dir) */ | |
| struct box *cube; | |
| unsigned char dir; | |
| int pos; | |
| long int mmt[33][33][33]; | |
| { | |
| switch(dir){ | |
| case RED: | |
| return( mmt[pos][cube->g1][cube->b1] | |
| -mmt[pos][cube->g1][cube->b0] | |
| -mmt[pos][cube->g0][cube->b1] | |
| +mmt[pos][cube->g0][cube->b0] ); | |
| break; | |
| case GREEN: | |
| return( mmt[cube->r1][pos][cube->b1] | |
| -mmt[cube->r1][pos][cube->b0] | |
| -mmt[cube->r0][pos][cube->b1] | |
| +mmt[cube->r0][pos][cube->b0] ); | |
| break; | |
| case BLUE: | |
| return( mmt[cube->r1][cube->g1][pos] | |
| -mmt[cube->r1][cube->g0][pos] | |
| -mmt[cube->r0][cube->g1][pos] | |
| +mmt[cube->r0][cube->g0][pos] ); | |
| break; | |
| } | |
| } | |
| float Var(cube) | |
| /* Compute the weighted variance of a box */ | |
| /* NB: as with the raw statistics, this is really the variance * size */ | |
| struct box *cube; | |
| { | |
| float dr, dg, db, xx; | |
| dr = Vol(cube, mr); | |
| dg = Vol(cube, mg); | |
| db = Vol(cube, mb); | |
| xx = m2[cube->r1][cube->g1][cube->b1] | |
| -m2[cube->r1][cube->g1][cube->b0] | |
| -m2[cube->r1][cube->g0][cube->b1] | |
| +m2[cube->r1][cube->g0][cube->b0] | |
| -m2[cube->r0][cube->g1][cube->b1] | |
| +m2[cube->r0][cube->g1][cube->b0] | |
| +m2[cube->r0][cube->g0][cube->b1] | |
| -m2[cube->r0][cube->g0][cube->b0]; | |
| return( xx - (dr*dr+dg*dg+db*db)/(float)Vol(cube,wt) ); | |
| } | |
| /* We want to minimize the sum of the variances of two subboxes. | |
| * The sum(c^2) terms can be ignored since their sum over both subboxes | |
| * is the same (the sum for the whole box) no matter where we split. | |
| * The remaining terms have a minus sign in the variance formula, | |
| * so we drop the minus sign and MAXIMIZE the sum of the two terms. | |
| */ | |
| float Maximize(cube, dir, first, last, cut, | |
| whole_r, whole_g, whole_b, whole_w) | |
| struct box *cube; | |
| unsigned char dir; | |
| int first, last, *cut; | |
| long int whole_r, whole_g, whole_b, whole_w; | |
| { | |
| register long int half_r, half_g, half_b, half_w; | |
| long int base_r, base_g, base_b, base_w; | |
| register int i; | |
| register float temp, max; | |
| base_r = Bottom(cube, dir, mr); | |
| base_g = Bottom(cube, dir, mg); | |
| base_b = Bottom(cube, dir, mb); | |
| base_w = Bottom(cube, dir, wt); | |
| max = 0.0; | |
| *cut = -1; | |
| for(i=first; i<last; ++i){ | |
| half_r = base_r + Top(cube, dir, i, mr); | |
| half_g = base_g + Top(cube, dir, i, mg); | |
| half_b = base_b + Top(cube, dir, i, mb); | |
| half_w = base_w + Top(cube, dir, i, wt); | |
| /* now half_x is sum over lower half of box, if split at i */ | |
| if (half_w == 0) { /* subbox could be empty of pixels! */ | |
| continue; /* never split into an empty box */ | |
| } else | |
| temp = ((float)half_r*half_r + (float)half_g*half_g + | |
| (float)half_b*half_b)/half_w; | |
| half_r = whole_r - half_r; | |
| half_g = whole_g - half_g; | |
| half_b = whole_b - half_b; | |
| half_w = whole_w - half_w; | |
| if (half_w == 0) { /* subbox could be empty of pixels! */ | |
| continue; /* never split into an empty box */ | |
| } else | |
| temp += ((float)half_r*half_r + (float)half_g*half_g + | |
| (float)half_b*half_b)/half_w; | |
| if (temp > max) {max=temp; *cut=i;} | |
| } | |
| return(max); | |
| } | |
| int | |
| Cut(set1, set2) | |
| struct box *set1, *set2; | |
| { | |
| unsigned char dir; | |
| int cutr, cutg, cutb; | |
| float maxr, maxg, maxb; | |
| long int whole_r, whole_g, whole_b, whole_w; | |
| whole_r = Vol(set1, mr); | |
| whole_g = Vol(set1, mg); | |
| whole_b = Vol(set1, mb); | |
| whole_w = Vol(set1, wt); | |
| maxr = Maximize(set1, RED, set1->r0+1, set1->r1, &cutr, | |
| whole_r, whole_g, whole_b, whole_w); | |
| maxg = Maximize(set1, GREEN, set1->g0+1, set1->g1, &cutg, | |
| whole_r, whole_g, whole_b, whole_w); | |
| maxb = Maximize(set1, BLUE, set1->b0+1, set1->b1, &cutb, | |
| whole_r, whole_g, whole_b, whole_w); | |
| if( (maxr>=maxg)&&(maxr>=maxb) ) { | |
| dir = RED; | |
| if (cutr < 0) return 0; /* can't split the box */ | |
| } | |
| else | |
| if( (maxg>=maxr)&&(maxg>=maxb) ) | |
| dir = GREEN; | |
| else | |
| dir = BLUE; | |
| set2->r1 = set1->r1; | |
| set2->g1 = set1->g1; | |
| set2->b1 = set1->b1; | |
| switch (dir){ | |
| case RED: | |
| set2->r0 = set1->r1 = cutr; | |
| set2->g0 = set1->g0; | |
| set2->b0 = set1->b0; | |
| break; | |
| case GREEN: | |
| set2->g0 = set1->g1 = cutg; | |
| set2->r0 = set1->r0; | |
| set2->b0 = set1->b0; | |
| break; | |
| case BLUE: | |
| set2->b0 = set1->b1 = cutb; | |
| set2->r0 = set1->r0; | |
| set2->g0 = set1->g0; | |
| break; | |
| } | |
| set1->vol=(set1->r1-set1->r0)*(set1->g1-set1->g0)*(set1->b1-set1->b0); | |
| set2->vol=(set2->r1-set2->r0)*(set2->g1-set2->g0)*(set2->b1-set2->b0); | |
| return 1; | |
| } | |
| Mark(cube, label, tag) | |
| struct box *cube; | |
| int label; | |
| unsigned char *tag; | |
| { | |
| register int r, g, b; | |
| for(r=cube->r0+1; r<=cube->r1; ++r) | |
| for(g=cube->g0+1; g<=cube->g1; ++g) | |
| for(b=cube->b0+1; b<=cube->b1; ++b) | |
| tag[(r<<10) + (r<<6) + r + (g<<5) + g + b] = label; | |
| } | |
| int | |
| main () | |
| { | |
| struct box cube[MAXCOLOR]; | |
| unsigned char *tag; | |
| unsigned char lut_r[MAXCOLOR], lut_g[MAXCOLOR], lut_b[MAXCOLOR]; | |
| int next; | |
| register long int i, weight; | |
| register int k; | |
| float vv[MAXCOLOR], temp; | |
| /* input R,G,B components into Ir, Ig, Ib; | |
| set size to width*height */ | |
| printf("no. of colors:\n"); | |
| scanf("%d", &K); | |
| Hist3d(wt, mr, mg, mb, m2); printf("Histogram done\n"); | |
| free(Ig); free(Ib); free(Ir); | |
| M3d(wt, mr, mg, mb, m2); printf("Moments done\n"); | |
| cube[0].r0 = cube[0].g0 = cube[0].b0 = 0; | |
| cube[0].r1 = cube[0].g1 = cube[0].b1 = 32; | |
| next = 0; | |
| for(i=1; i<K; ++i){ | |
| if (Cut(&cube[next], &cube[i])) { | |
| /* volume test ensures we won't try to cut one-cell box */ | |
| vv[next] = (cube[next].vol>1) ? Var(&cube[next]) : 0.0; | |
| vv[i] = (cube[i].vol>1) ? Var(&cube[i]) : 0.0; | |
| } else { | |
| vv[next] = 0.0; /* don't try to split this box again */ | |
| i--; /* didn't create box i */ | |
| } | |
| next = 0; temp = vv[0]; | |
| for(k=1; k<=i; ++k) | |
| if (vv[k] > temp) { | |
| temp = vv[k]; next = k; | |
| } | |
| if (temp <= 0.0) { | |
| K = i+1; | |
| fprintf(stderr, "Only got %d boxes\n", K); | |
| break; | |
| } | |
| } | |
| printf("Partition done\n"); | |
| /* the space for array m2 can be freed now */ | |
| tag = (unsigned char *)malloc(33*33*33); | |
| if (tag==NULL) {printf("Not enough space\n"); exit(1);} | |
| for(k=0; k<K; ++k){ | |
| Mark(&cube[k], k, tag); | |
| weight = Vol(&cube[k], wt); | |
| if (weight) { | |
| lut_r[k] = Vol(&cube[k], mr) / weight; | |
| lut_g[k] = Vol(&cube[k], mg) / weight; | |
| lut_b[k] = Vol(&cube[k], mb) / weight; | |
| } | |
| else{ | |
| fprintf(stderr, "bogus box %d\n", k); | |
| lut_r[k] = lut_g[k] = lut_b[k] = 0; | |
| } | |
| } | |
| for(i=0; i<size; ++i) Qadd[i] = tag[Qadd[i]]; | |
| /* output lut_r, lut_g, lut_b as color look-up table contents, | |
| Qadd as the quantized image (array of table addresses). */ | |
| } |
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Code works well... got it working in .Net with visual studio 2015 in ~ hour.
Had to change a few things (ie K & R style header)... and made main a function.
ifndef DWORD
endif
DWORD x_wu_main(DWORD update, DWORD *p_Idata, DWORD *p_IDest, DWORD p_size, DWORD pal_colors, DWORD *pal);
include "stdafx.h"
include "LCD Maker Support.h"
include <memory.h>
include <malloc.h>
/**********************************************************************
C Implementation of Wu's Color Quantizer (v. 2)
(see Graphics Gems vol. II, pp. 126-133)
Author: Xiaolin Wu
Dept. of Computer Science
Univ. of Western Ontario
London, Ontario N6A 5B7
[email protected]
Algorithm: Greedy orthogonal bipartition of RGB space for variance
minimization aided by inclusion-exclusion tricks.
For speed no nearest neighbor search is done. Slightly
better performance can be expected by more sophisticated
but more expensive versions.
The author thanks Tom Lane at [email protected] for much of
additional documentation and a cure to a previous bug.
Free to distribute, comments and suggestions are appreciated.
**********************************************************************/
include <stdio.h>
define MAXCOLOR 256
define RED 2
define GREEN 1
define BLUE 0
struct box
{
int r0;
int r1;
int g0;
int g1;
int b0;
int b1;
int vol;
};
typedef struct box _BOX;
/* Histogram is in elements 1..HISTSIZE along each axis,
*/
float m2[33][33][33];
int wt[33][33][33];
int mr[33][33][33];
int mg[33][33][33];
int mb[33][33][33];
// These items set from main
DWORD _Idata; // 32 bit pointer to ARGB
int size; // how many ARGB items
int K; /_color look-up table size*/
USHORT *Qadd;
bool Hist3d(int *vwt, int *vmr, int *vmg, int *vmb, float *m2)
{
int ind, r, g, b;
int inr, ing, inb, table[256];
int i;
}
/* At conclusion of the histogram step, we can interpret
*/
/* We now convert histogram into moments so that we can rapidly calculate
*/
void M3d(int vwt, int *vmr, int *vmg, int *vmb, float *m2) / compute cumulative moments. */
{
unsigned short int ind1, ind2;
unsigned char i, r, g, b;
int line, line_r, line_g, line_b, area[33], area_r[33], area_g[33], area_b[33];
float line2, area2[33];
}
int Vol(_BOX cube, int mmt[33][33][33]) / Compute sum over a box of any given statistic */
{
return (mmt[cube->r1][cube->g1][cube->b1]
- mmt[cube->r1][cube->g1][cube->b0]
- mmt[cube->r1][cube->g0][cube->b1]
+ mmt[cube->r1][cube->g0][cube->b0]
- mmt[cube->r0][cube->g1][cube->b1]
+ mmt[cube->r0][cube->g1][cube->b0]
+ mmt[cube->r0][cube->g0][cube->b1]
- mmt[cube->r0][cube->g0][cube->b0]);
}
/* The next two routines allow a slightly more efficient calculation
of Vol() for a proposed subbox of a given box. The sum of Top()
and Bottom() is the Vol() of a subbox split in the given direction
and with the specified new upper bound.
*/
int Bottom(_BOX cube, unsigned char dir, int mmt[33][33][33]) / Compute part of Vol(cube, mmt) that doesn't depend on r1, g1, or b1 (depending on dir) */
{
if (dir == RED)
{
return -mmt[cube->r0][cube->g1][cube->b1] + mmt[cube->r0][cube->g1][cube->b0] + mmt[cube->r0][cube->g0][cube->b1] - mmt[cube->r0][cube->g0][cube->b0];
}
else if (dir == GREEN)
{
return -mmt[cube->r1][cube->g0][cube->b1] + mmt[cube->r1][cube->g0][cube->b0] + mmt[cube->r0][cube->g0][cube->b1] - mmt[cube->r0][cube->g0][cube->b0];
}
else
{
return -mmt[cube->r1][cube->g1][cube->b0] + mmt[cube->r1][cube->g0][cube->b0] + mmt[cube->r0][cube->g1][cube->b0] - mmt[cube->r0][cube->g0][cube->b0];
}
}
int Top(_BOX cube, BYTE dir, int pos, int mmt[33][33][33]) / Compute remainder of Vol(cube, mmt), substituting pos for r1, g1, or b1 (depending on dir) */
{
if (dir == RED)
{
return mmt[pos][cube->g1][cube->b1] - mmt[pos][cube->g1][cube->b0] - mmt[pos][cube->g0][cube->b1] + mmt[pos][cube->g0][cube->b0];
}
else if (dir == GREEN)
{
return mmt[cube->r1][pos][cube->b1] - mmt[cube->r1][pos][cube->b0] - mmt[cube->r0][pos][cube->b1] + mmt[cube->r0][pos][cube->b0];
}
else
{
return mmt[cube->r1][cube->g1][pos] - mmt[cube->r1][cube->g0][pos] - mmt[cube->r0][cube->g1][pos] + mmt[cube->r0][cube->g0][pos];
}
}
float Var(_BOX cube) / Compute the weighted variance of a box - NB: as with the raw statistics, this is really the variance * size */
{
int dr = Vol(cube, mr);
int dg = Vol(cube, mg);
int db = Vol(cube, mb);
}
/* We want to minimize the sum of the variances of two subboxes.
*/
float Maximize(_BOX *cube, unsigned char dir, int first, int last, int *cut, int whole_r, int whole_g, int whole_b, int whole_w)
{
int base_r = Bottom(cube, dir, mr);
int base_g = Bottom(cube, dir, mg);
int base_b = Bottom(cube, dir, mb);
int base_w = Bottom(cube, dir, wt);
}
int Cut(_BOX *set1, _BOX *set2)
{
BYTE dir;
int cutr, cutg, cutb;
}
void Mark(_BOX *cube, int label, BYTE *tag)
{
for (int r = cube->r0 + 1; r <= cube->r1; r++)
{
for (int g = cube->g0 + 1; g <= cube->g1; g++)
{
for (int b = cube->b0 + 1; b <= cube->b1; b++)
{
tag[(r << 10) + (r << 6) + r + (g << 5) + g + b] = label;
}
}
}
}
DWORD x_wu_main(DWORD update_bmp, DWORD *p_Idata, DWORD *p_IDest, DWORD p_size, DWORD pal_colors, DWORD *pal)
{
_BOX cube[MAXCOLOR];
BYTE *tag;
BYTE lut_r[MAXCOLOR], lut_g[MAXCOLOR], lut_b[MAXCOLOR];
}